:minimalist

Monday, February 24, 2014

 

The other day I was explaining the prominence of I, IV, V, and vi chords in popular music to someone and explaining how you can use this fact to guess at which chord will come next in whatever song you are trying to reverse engineer. Although I didn't mention it at the time (seemed a bit of a stretch for talking to a 13-year-old), it occurred to me that this is very similar to how differential equations was taught to me - with a known set of high probability solutions, pick one and plug it in and see if it works.

With sufficient practice, arriving at the correct answer on the first guess becomes a matter of intuition. In reality, both problems (music and differential equations) are more nuanced, and there are further heuristics that you can use to refine your guess before checking. To the unpracticed observer, though, I suppose it all seems a bit mysterious.

Playing a song by ear is a useful skill to me. Solving differential equations on the first try, not so much.

bananna 6:37 PM  |